Find the derivative of $y=\left(x^{2}-4 x+9\right)\left(3 x^{2}+10\right)$.
A) $\frac{d y}{d x}=3 x^{3}-24 x^{2}+54 x-4$
B) $\frac{d y}{d x}=12 x^{2}+24 x$
C) $\frac{d y}{d x}=6 x^{3}-12 x^{2}+20 x-40$
D) $\frac{d y}{d x}=12 x^{3}-36 x^{2}+74 x-40$

Question

Quizplus · Accepted Answer

The derivative is found using the product rule: $(u \cdot v)' = u'v + uv'$. Here, $u = x^2 - 4x + 9$ and $v = 3x^2 + 10$. Calculating $u'$ and $v'$, and applying the product rule gives the derivative as $12x^3 - 36x^2 + 74x - 40$.

Find the Derivative Of y=(x2−4x+9)(3x2+10)y=\left(x^{2}-4 x+9\right)\left(3 x^{2}+10\right)y=(x2−4x+9)(3x2+10) A) dydx=3x3−24x2+54x−4\frac{d y}{d x}=3 x^{3}-24 x^{2}+54 x-4dxdy​=3x3−24x2+54x−4

Find the Derivative Of $y=\left(x^{2}-4 x+9\right)\left(3 x^{2}+10\right)$
A) $\frac{d y}{d x}=3 x^{3}-24 x^{2}+54 x-4$